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When \( x_1 = 0 \), the values of the other variables depend on \( x_6 \). The solutions are expressed as follows:

- \( x_2 = -170 \)
- \( x_3 = x_6 - 100 \)
- \( x_4 = x_6 - 200 \)
- \( x_5 = x_6 - 200 \)

To fully determine the values of \( x_3 \), \( x_4 \), and \( x_5 \), you would need to specify a value for \( x_6 \).

Would you like more details or have any questions? Here are 5 related questions:

1. What happens to the system if \( x_6 = 0 \)?
2. Can we simplify the system if \( x_6 \) takes a specific value?
3. How would the solution change if \( x_1 \) had a different value?
4. What is the role of \( x_4 \) and \( x_5 \) being equal in the system?
5. How can this system be solved using matrix methods?

**Tip:** When solving systems with undetermined variables, sometimes setting specific values can simplify the process.

This problem involves solving a system of equations where x1 is set to 0. By substituting values, we can express other variables such as x2, x3, x4, and x5 in terms of x6. Explore how linear algebra techniques are used to simplify and solve such systems.

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